Question

You set up a college fund in which you pay $5,000 each year at the beginning of the year. how much money will you have accumulated in the fund after 25 years, if your fund earns 10% compounded annually?

Answer 1

To calculate the accumulated amount in the fund after 25 years, we can use the formula for compound interest. With an annual payment of $5,000 and an interest rate of 10% compounded annually, the accumulated amount will be approximately $33,160.74.

Step-by-step explanation:

To calculate the accumulated amount in the fund, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• A is the accumulated amount
• P is the annual payment
• r is the interest rate in decimal form
• n is the number of times interest is compounded per year
• t is the number of years

In this case:

• P = $5,000
• r = 10% = 0.10
• n = 1 (compounded annually)
• t = 25 years

Substituting these values into the formula, we get:

A = $5,000(1 + 0.10/1)^(1*25)

Simplifying the expression:

A = $5,000(1.10)^25

Using a calculator:

A ≈ $33,160.74

Therefore, you will have accumulated approximately $33,160.74 in the college fund after 25 years.